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arXiv · 2507.22721

Continuity of critical points for 1-dimensional non-local energies

Davide Carazzato·Nicola Fusco·Aldo Pratelli
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Abstract

In this paper we deal with the bounded critical points of a Riesz energy of attractive-repulsive type in dimension 1. Under suitable assumptions on the growth of the kernel in the origin, we are able to prove that they are continuous inside their support.

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Davide Carazzato, Nicola Fusco, Aldo Pratelli. 2025-07-30. Continuity of critical points for 1-dimensional non-local energies. https://doi.org/10.1515/acv-2025-0094

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